Singularity-free analytical energy gradients for the SAC/SAC-CI method: coupled perturbed minimum orbital-deformation (CPMOD) approach

A new procedure for evaluating energy gradients in a singularity-free manner is presented for use in the SAC/SAC-CI program in which computational dimensions are reduced by the perturbation selection method. The singularity in the energy gradients stemming from a breakdown of the unitary invariance is effectively removed by the minimum orbital-deformation (MOD) method proposed in the previous study. All calculations can be done analytically via new two sets of linear equations combined with the coupled-perturbed Hartree–Fock method. Geometry optimizations for malonaldehyde in the ground and lowest singlet excited states are performed by the new method.